Did shahjehan really want to construct a black taj mahal infront of the white marbel taj mahal or it isjust a myth?

The Taj Mahal of Agra is one fine example of how to plan and then successfully apply symmetry into the proceedings. Every inch of Taj Mahal is a breathing example of it, except for one thing: the cenotaph of Shah Jahan himself, which appears to be an afterthought as it was added much later and disassembles the symmetry of the burial chamber as it is bigger in size when compared to the cenotaph of Mumtaz Mahal. Ever wondered why is this the only dissymmetrical thing in the entire Taj complex? Some scholars believe that Shah Jahan had never meant for himself to be buried along with his wife but was planning something big. Scholars believe this "something big" to be another Taj Mahal, but built in black marble instead of white. According to the Black Taj myth, Shah Jahan had planned to build mirror image of the Taj Mahal he built for Mumtaz, albeit in black, on the other side of the river and connect the two by a bridge. This Black Taj was to be dedicated to Shah Jahan himself. A European traveler by the name of Jean Baptiste Tavernier who visited Agra in 1665 first mentioned the idea of Black Taj in his fanciful writings. And considering Shah Jahan's obsession with symmetry, the idea certainly seems plausible. More credibility to the story is added by an observation made by archeologists in 2006, when they reconstructed part of the pool in the moonlit garden and it reflected a dark reflection of the white mausoleum. The writings of Tavernier mention that Shah Jahan began to build his own tomb on the other side of the river but could not complete it as he was deposed by his own son Aurangzeb.